Preamble

A Study on the Long-Term Variation of Signal Current in Rhodium Self-Powered Neutron Detectors Under In-Core Burnup Conditions
Zhiqi Guo¹,²,³, Wenhua Yang³, Shuo Zhang¹,², Zhan Li¹,², Jingyi Han¹,², Chunhui Zhang¹,², Dingjun Zhu¹,², Jianxiong Shao¹,²*

¹School of Nuclear Science and Technology, Lanzhou University, Gansu, PR China
³Nuclear Power Institute of China, Chengdu, Sichuan, China

Abstract: As a key instrument for measuring neutron flux within a reactor core, the signal current of a Self-Powered Neutron Detector (SPND) evolves continuously due to material burnup during operation. Accurately accounting for this long-term variation is essential for reliable power monitoring and safe reactor operation. This study focuses on Rhodium Self-Powered Neutron Detectors (Rh-SPNDs) and develops a predictive model for signal current variation using a Back Propagation Neural Network (BPNN) within the context of a typical Pressurized Water Reactor (PWR). The model incorporates changes in emitter material composition due to burnup and employs a layered approach to calculate radial burnup distribution. Key parameters including beta electron generation rate, escape probability, gamma photon generation, and gamma-induced electron escape rate are systematically considered. Results demonstrate that over a 10-year period at a neutron flux of 1×10¹⁴ n/(cm²·s), smaller rhodium wire radii exhibit greater sensitivity variation. Specifically, a 0.1 mm wire radius yields a 51.3% sensitivity reduction, while a 1 mm radius yields a 25.2% reduction. The proposed model enables accurate sensitivity compensation for Rh-SPNDs over time, thereby minimizing neutron flux measurement errors and enhancing reactor safety and stability.

Keywords: Rh-SPND; Burnup; Long-Term Signal Current Evolution; BPNN; Prediction Model

1 Introduction

The neutron flux within a reactor core is intimately linked to safe and stable reactor operation as well as power density mapping [1]. Consequently, real-time monitoring of in-core neutron flux is of paramount importance [2]. Among the tools available for online neutron flux monitoring, the Self-Powered Neutron Detector (SPND) has found widespread application in both research and commercial reactors [3]. Compared with traditional fission chambers and activation neutron detectors, SPNDs offer several advantages, including no requirement for external power, simple structure, compact size, and ease of installation [4]. However, during in-core service, the SPND emitter continuously undergoes neutron-induced reactions, resulting in progressive material depletion and gradual signal current deviation over time [5]. To achieve real-time and accurate monitoring of core neutron flux, proper accounting for SPND burnup is therefore crucial [6]. Yaodong Sang et al. investigated Ag-SPND burnup and found that after 10.5 years of operation, neutron sensitivity decreased by 16.68%, while sensitivity to external gamma rays remained essentially unchanged throughout the entire period [7].

A. A. Khrutchinsky studied Rh-SPND emitter burnup in a VVER-1000 reactor using Monte Carlo simulations, discovering that after 10.5 years of irradiation, over 90% of ¹⁰³Rh had been consumed and sensitivity dropped to 10% of its initial value. Additionally, burnup produced a non-uniform radial density distribution in the emitter, with outer layers experiencing higher burnup rates than inner regions [8]. Hyunsuk Lee proposed a new sensitivity calculation model based on Monte Carlo simulations and continuous-spectrum neutrons, which verified Rh-SPND sensitivity attenuation under high burnup conditions, showing consistency with EPRI empirical data [9]. A. Yu. Kurchenkov introduced a novel method for determining reactor core thermal power by more accurately defining SPND burnup as a function of transmitted power, thereby reducing errors in measuring local core parameters [10].

As SPNDs undergo continuous burnup within the reactor core, emitter material composition changes accordingly, affecting both neutron capture rates and electron escape probabilities, which in turn alters SPND signal current. The increasing complexity and diversity of emitter composition during burnup, combined with neutron self-shielding effects that produce uneven burnup between inner and outer emitter layers, render electron generation and escape rates non-uniform throughout the emitter. Under these multiple uncertainties, traditional numerical calculations struggle to systematically and comprehensively analyze SPND signal current variation with burnup. Back Propagation Neural Networks have emerged as an important tool in nuclear technology for processing detector signals and similar data, particularly for handling complex nonlinear relationships [11]. This study focuses on Rhodium Self-Powered Neutron Detectors (Rh-SPNDs), investigating rhodium wire burnup and material composition evolution over time based on the Hualong One reactor design, and employs a combination of Monte Carlo methods and BPNN to examine the variation of Rh-SPND signal current with burnup.

2.1 Overview of Rhodium Self-Powered Neutron Detector (Rh-SPND)

As illustrated in Fig. 1 [FIGURE:1], a self-powered neutron detector probe typically consists of three components: the emitter, insulator, and collector. The emitter represents the core component that determines the detector's fundamental characteristics. The SPND operating principle relies on nuclear reactions between emitter material and neutrons to generate free electrons [12]. These electrons traverse the insulator and reach the collector, causing the emitter to become positively charged and the insulator negatively charged, thereby forming positive and negative poles through which the electrical signal can be transmitted via a wire. Common SPND emitter materials include vanadium, cobalt, rhodium, and silver. Among these, rhodium possesses a large neutron reaction cross-section and produces strong current signals, but also burns out more rapidly in the reactor environment. Therefore, ensuring real-time and accurate monitoring of core neutron flux necessitates in-depth study of Rh-SPND signal current variation with burnup time.

2.2 Overall Research Methodology

The overall methodology adopted in this study is structured into four major stages, schematically depicted in Fig. 2 [FIGURE:2]. Stage 1 involves burnup simulation via Monte Carlo modeling, where a detailed SPND emitter burnup model is constructed to calculate time-dependent changes in isotopic and elemental composition during extended reactor operation, considering actual operating conditions including neutron flux levels and energy spectra. Stage 2 focuses on sensitivity variation computation, calculating the Rh-SPND sensitivity—defined as the ratio of signal current to neutron flux—for detectors with fixed geometries to determine how sensitivity evolves as a function of burnup time, accounting for the changing composition and geometry of the emitter. Stage 3 encompasses development and training of a predictive BPNN model, where a comprehensive dataset generated from Monte Carlo simulation results is used to train a network designed to learn complex nonlinear relationships between input variables (burnup time, emitter radius, emitter layer count) and output characteristics (beta electron yield, gamma photon generation, escape probabilities). Stage 4 employs the trained BPNN model to predict signal currents for Rh-SPNDs of various geometries under different burnup levels, enabling estimation of detector performance over time and facilitating improved compensation strategies for reliable flux monitoring in nuclear reactors. Through this structured, multi-layered research framework, the study aims to provide a quantitative and systematic solution to the challenge of long-term Rh-SPND signal evolution, ensuring more accurate and robust neutron flux measurements during prolonged reactor operation.

3.1 Generation and Calculation Method of Burnup

The emitter material within an SPND undergoes progressive neutron-induced depletion, commonly referred to as burnup, as it continuously absorbs neutrons during reactor operation. This process results in a steady decline in SPND neutron sensitivity over time. To mitigate sensitivity degradation caused by material consumption, accurate calculation of emitter burnup rate is essential for predicting changes in detector signal current. The burnup of a self-powered detector can be approximated using the following equation (1) [13]:

$$N(t) = N_0 \exp(-\sigma_{\text{eff}} \phi_f t)$$

Where: N represents the number of atoms in the emitter at time t; N₀ represents the number of atoms in the emitter at the initial time; σ_eff is the effective neutron capture cross-section; φ_f is the average neutron flux in the reactor, with units of n/(cm²·year). This mathematical formulation assumes a continuous irradiation environment and neglects short-term operational fluctuations, which is generally acceptable for long-term modeling of in-core detector behavior.

3.2 Layered Burnup Calculation Model

A significant portion of the Rh-SPND signal originates from beta electrons released during radioactive decay of activated rhodium isotopes. Therefore, effective analysis of long-term signal variation requires accurate determination of emitter material composition at various burnup stages, necessitating a high-resolution spatial model of the emitter. The emitter typically features cylindrical geometry, and due to neutron self-shielding effects, burnup distribution is inherently non-uniform across the emitter's radial profile. Over time, outer emitter layers absorb more neutrons, leading to higher local burnup rates than inner regions. This spatial discrepancy alters not only nuclide distribution but also the distribution of beta electron generation and escape probabilities across the emitter cross-section. To capture this radial heterogeneity, a layered model is employed, as depicted in Fig. 3 [FIGURE:3], where the emitter is divided into multiple concentric layers analyzed independently for burnup level and electron escape characteristics. This modeling strategy enhances computational precision and enables more accurate estimation of the detector's net current response.

Given that SPNDs operate directly within the reactor core environment, burnup simulation must reflect realistic operating conditions, including reactor-specific neutron flux spectra and geometry. This study selects the Hualong One Pressurized Water Reactor (PWR) as the reference model. Fig. 4 [FIGURE:4] presents a schematic diagram of a Hualong One fuel assembly along with the neutron energy spectrum within the instrumentation channel where the SPND is embedded. The rhodium wire is modeled within this guide tube, and burnup simulations are conducted using the Monte Carlo N-Particle (MCNP) transport code, utilizing the burn card feature to track isotopic depletion and transmutation over time, thereby quantifying both elemental composition and nuclide inventory after specified burnup intervals.

Using a rhodium wire with a radius of 0.4 mm as the representative case, the material and geometric parameters used in the simulation are summarized in Table 1 [TABLE:1]. The neutron energy spectrum derived from Fig. 4 is applied as the input source, and the core neutron flux is set to 1×10¹⁴ n/(cm²·s). Based on these inputs, the MCNP code simulates emitter burnup evolution over a 10-year period, with results plotted in Fig. 5 [FIGURE:5], which illustrates spatial variation in burnup across the emitter radius. The variable R/R₀ is defined, where R₀ is the total emitter radius and R is the distance from the emitter center. The plot shows that as R/R₀ increases, burnup also increases, confirming non-uniform radial behavior due to neutron attenuation in the material. After 10 years, the outermost layer exhibits a burnup level 66% higher than that of the innermost layer, highlighting the necessity of using layered models to accurately account for spatial effects in emitter degradation and signal prediction.

3.3 Material Composition of Rh-SPND After a Certain Burnup Duration

The burnup card output from MCNP provides detailed information on Rh-SPND nuclide composition after specified irradiation periods. For ¹⁰³Rh, a key emitter isotope, the complete reaction chain is shown in Fig. 6 [FIGURE:6], which includes isotopic transmutation and radioactive decay pathways such as (n, γ), (n, α), (n, p), (n, nα), and β-decay processes. These reaction chains produce a wide variety of secondary nuclides, some of which are radioactive and continue contributing to signal current via their own decay emissions. Using the rhodium wire with a radius of 0.4 mm, mass fractions of various nuclides are tracked over time as shown in Fig. 7 [FIGURE:7]. To assess burnup impact on signal current, particular attention is paid to nuclides exhibiting both high abundance and significant neutron cross-sections, as these most likely influence overall SPND performance.

The primary radioactive products of ¹⁰³Rh burnup include ¹⁰⁴Rh, ¹⁰⁵Rh, ¹⁰³Ru, ⁹⁹Tc, and ¹⁰⁰Tc, with half-lives ranging from seconds to hundreds of thousands of years. However, ¹⁰⁰Tc is excluded from consideration due to its extremely low abundance (below 1×10⁻¹⁰). In terms of stable and long-lived isotopes, nuclides such as ¹⁰⁴Pd, ¹⁰⁵Pd, ¹⁰⁶Pd, and ¹⁰⁴Ru remain present in considerable amounts post-burnup. These isotopes directly affect emitter mass, density, beta emission rate, and electron escape behavior, and must therefore be accounted for in any accurate modeling of Rh-SPND long-term response.

4 Computational Model for the Sensitivity Variation of Rh-SPND with Burnup Time

The electrons contributing to Rh-SPND signal current can be categorized into three components: (a) electrons emitted from the decay of ¹⁰⁴Rh and ¹⁰⁴mRh produced through the (n, γ) reaction between neutrons and rhodium, referred to as delayed current and constituting the primary signal component; (b) electrons generated via photoelectric effect, Compton scattering, and pair production caused by gamma photons from the (n, γ) reaction between neutrons and rhodium, called prompt current and contributing a smaller fraction; and (c) electrons generated by interaction of reactor gamma photons with the Rh-SPND through photoelectric effect, Compton scattering, and pair production, considered interference current that must be subtracted from the total current. The sensitivity of a self-powered neutron detector is defined as the ratio of Rh-SPND signal current to neutron flux surrounding the detector:

$$S = \frac{I}{\phi_n} = \frac{I_b + I_g}{\phi_n}$$

Where: I denotes the signal current, S is the sensitivity coefficient of the Rh-SPND, φ_n is the neutron flux; I_b is the current generated by beta electrons, I_g is the current generated by gamma radiation.

4.1 Computational Model for the Variation of Delayed Current with Burnup

The delayed current is primarily produced from the decay of ¹⁰⁴Rh and can be expressed as:

$$I_b = e \cdot R_b \cdot P_{be}$$

Where: e is the elementary charge, valued at 1.60×10⁻¹⁹ C; R_b represents the generation rate of beta electrons within the entire emitter; P_be denotes the escape probability of the electrons.

4.1.1 Variation of Neutron Capture Rate with Burnup Time

To investigate spatial variation of neutron absorption in the emitter, a rhodium wire with a radius of 0.4 mm is analyzed. Due to neutron self-shielding effects, neutron flux attenuates as it penetrates radially inward, leading to non-uniform burnup across the emitter cross-section. To quantitatively model this phenomenon, the rhodium wire is divided into 10 concentric layers, with layer 1 located at the central axis and layer 10 on the outermost surface. Burnup level and composition of each layer are derived from prior Monte Carlo simulations. As shown in Fig. 8 FIGURE:8, pronounced differences in neutron capture rate exist across layers. After 10 years of irradiation, the innermost layer shows an 18% change, while the outermost layer experiences a 96% change. This gradient highlights the strong influence of spatial position on neutron-induced transmutation. Fig. 8(b) presents each layer's contribution to the total neutron capture rate as a function of time. The outermost layer's contribution declines steadily, while inner layers contribute increasingly over time. This shift in neutron absorption leads to gradual inward migration of the beta electron production centroid, which must be considered in dynamic sensitivity modeling.

4.1.2 Escape Probability of Beta Electrons

The escape probability of electrons in the emitter depends on electron position, energy, and emitter material composition. Using a rhodium wire with a radius of 0.4 mm as the research object, it is divided into 10 layers. Calculations employ the Geant4 program, with material composition of different rhodium wire layers taken from the results in Fig. 7 as input data. When calculating beta electron escape probability, electron energy must be specified. Beta electrons are primarily generated by ¹⁰⁴Rh decay. However, after the rhodium wire has burned for some time, other radioactive nuclides such as ¹⁰⁵Rh, ¹⁰³Ru, and ⁹⁹Tc are also produced. Table 2 [TABLE:2] lists the variation in activity of these four radioactive nuclides with burnup time. According to the data, ¹⁰⁴Rh activity is at least 4-5 orders of magnitude higher than that of the other radioactive nuclides. This magnitude difference allows the influence of radioactive nuclides other than ¹⁰⁴Rh to be excluded when setting beta electron energy in Geant4. Fig. 9 [FIGURE:9] shows the escape probability of beta electrons for different burnup times and different layers. The figure reveals that changes in material composition caused by rhodium wire burnup have essentially no effect on beta electron escape probability. This is because when electrons escape from inside the emitter to the surface, energy loss occurs primarily through ionization and radiation. When electron energy remains unchanged, energy loss through ionization and radiation depends mainly on the atomic number and density of the target material. The atomic number of burnup products varies within a range of ±2, and emitter density change is also very small. Therefore, burnup-induced changes in material composition have essentially no effect on beta electron escape probability. This conclusion allows decoupling of escape probability from burnup composition in subsequent modeling steps.

4.2 Computational Model for the Variation of Prompt Current with Burnup

Prompt current is generated by electrons produced through photoelectric effect and Compton scattering when gamma rays interact with the emitter. It can be expressed as:

$$I_g = e \cdot P_g \cdot P_{eR} \cdot P_{ee}$$

Where: e is the elementary charge, P_g denotes the probability of gamma ray production from neutron interactions within the emitter, P_{eR} denotes the probability that gamma rays generate electrons in the emitter, P_{ee} denotes the escape probability of electrons generated by gamma rays.

4.2.1 Variation of Gamma Ray Yield with Burnup Time

The fast response component in Rh-SPND signal current is generated by interaction of gamma photons with the detector. This current component also changes with burnup time and therefore requires calculation. Prompt gamma rays in Rh-SPND are primarily generated by the (n, γ) reaction between neutrons and Rh-SPND materials. Additionally, radioactive nuclides emit gamma rays during decay due to energy level transitions. These delayed gamma rays account for a relatively low proportion. Since reaction cross-sections of collector and insulator materials with neutrons are low, only variation of gamma ray yield from the emitter with burnup time is considered. Fig. 10 FIGURE:10 shows the gamma photon spectrum in different emitter layers after 1 year of burnup. Fig. 10(b) shows variation of gamma photon generation rate with burnup time. The generation rate continuously decreases with burnup time, with the first layer decreasing slowest (21% decrease from year 1 to year 10) and the tenth layer decreasing fastest (25% decrease from year 1 to year 10). Compared to the large difference in neutron capture rate between inner and outer layers, the change in gamma photon generation rate between inner and outer layers is basically consistent. This is because neutron capture rate represents only neutron capture by ¹⁰³Rh, while gamma photon generation rate results from reaction of the entire emitter material with neutrons, including gamma photons from (n, γ) reactions of other nuclides produced after burnup. Delayed gamma ray yield accounts for about 1.2% of total gamma rays, and the contribution of electrons generated by their interaction with the detector to the total current signal can be neglected. Therefore, variation of delayed gamma rays with burnup time is not considered.

4.2.2 Variation of Probability of Electron Generation by Gamma Rays with Burnup

The probability of gamma rays interacting with the emitter to generate electrons is primarily affected by electron energy and the atomic number of the target material. Emitter burnup changes material composition, affecting electron generation rate. Therefore, calculation of the variation in electron generation probability by gamma rays with burnup time is necessary. As shown in Fig. 11 [FIGURE:11], as burnup time increases, the electron generation rate continuously increases, with the innermost layer showing the largest change and the outermost layer's electron generation rate remaining basically unchanged. The electron generation rate varies significantly between different layers, decreasing continuously as R/R₀ increases. This is because the path length traveled by gamma photons in the emitter differs; larger R/R₀ values correspond to shorter paths, fewer collisions with the emitter, and thus fewer electrons generated.

4.2.3 Escape Probability of Electrons Generated by Gamma Rays

Prompt gamma rays interact with the emitter through Compton and photoelectric effects to generate electrons, forming the instantaneous response current. The escape probability of these electrons is affected by the gamma ray spectrum and their generation position within the emitter. Using the spectrum in Fig. 10(a) as the input source, the electron escape rate is calculated. Fig. 12 FIGURE:12 shows the electron spectrum generated by gamma photons interacting with the emitter through photoelectric effect, Compton effect, and electron pair effect. The escape probability of electrons generated by gamma rays is shown in Fig. 12(b). Similar to beta electron escape probability, larger R/R₀ values yield greater electron escape probability. Moreover, changes in rhodium wire composition due to burnup time have basically no effect on electron escape probability. The reasons for this have been discussed in the section on beta electron escape probability and will not be repeated here.

4.3 Influence of Gamma Rays in the Reactor on Rh-SPND Signal Current

Gamma rays within the reactor originate from nuclear fuel fission and reactions between neutrons and other reactor materials. Changes due to Rh-SPND burnup do not affect their spectrum or flux. Therefore, this section mainly discusses the electron generation rate from interaction of reactor gamma rays with the emitter at different burnup times. The gamma photon spectrum within the reactor is shown in Fig. 13 FIGURE:13. Using this as the input source, the electron generation rate is calculated. Taking the probability of electron generation from interaction of reactor photons with the emitter before rhodium wire burnup as the baseline, the change in electron generation rate due to emitter burnup at different times is calculated. The calculation results are shown in Fig. 13(b) [14]. The deviation in electron generation rate due to burnup is within ±4%, while the signal current generated by reactor gamma rays accounts for 5%-8% of the total current signal [15]. The error in this current component caused by burnup will contribute no more than 0.3% to the total Rh-SPND current signal. To improve computational efficiency and reduce unnecessary calculations, this burnup-induced error will not be considered in subsequent predictive model calculations.

5.1 Introduction to BP Neural Network

The Backpropagation Neural Network is a type of multi-layer feedforward network trained according to the error backpropagation algorithm [16]. This network is characterized by its nonlinear mapping capability and flexibility, allowing its structure to be adjusted according to problem requirements. The BP neural network consists of an input layer, hidden layer(s), and an output layer, where the hidden layer can comprise one or more layers [17]. Fig. 14 [FIGURE:14] shows the structure of a typical three-layer BP neural network. X_i represents the input layer, w_{ij} is the weight coefficient from input layer to hidden layer, θ_j is the threshold of the hidden layer, h is the activation function of the hidden layer, w_{jk} is the weight coefficient from hidden layer to output layer, a is the threshold of the output layer, f is the activation function of the output layer, and O is the actual output value.

5.2 BP Neural Network Model Training

Establishing a prediction model based on BPNN requires a foundation of training data calculated through preliminary Monte Carlo models. Only by training the BPNN with this data can the desired prediction model be obtained. In studying SPND signal current variation with burnup time, the actual relationship needed is the neutron sensitivity of detectors of different sizes at different burnup times. Therefore, for the BPNN, the input layer data are burnup time, emitter radius, and number of emitter layers, while the output layer data are neutron capture rate, beta electron escape rate, gamma photon generation rate, probability of electron generation by gamma photons, and escape rate of electrons generated by gamma photons. The burnup time range is 0-10 years. To calculate emitter material composition after burnup in greater detail, the time step is set to 1 quarter (3 months). Considering size differences, when layering the emitter, a step size of 0.05 mm is chosen, and the number of layers varies for emitters of different sizes.

Training the BP neural network requires determining the number of input layer nodes, hidden layers, hidden layer nodes, and output layer nodes. The number of input layer nodes is 3 and the number of output layer nodes is 5, which are already determined. The number of hidden layers depends on problem complexity. For relatively simple problems with not-too-large experimental sample sizes, the number of hidden layers is generally 1 or 2, and should not exceed 3 to avoid overfitting [18]. There is no theoretical guidance for choosing the number of hidden layer nodes. In deep networks, the number of nodes is usually reduced layer by layer, such as scaling down proportionally from input to output. The activation function between the hidden layer and output layer uses the Sigmoid function [19], whose expression is:

$$f(x) = \frac{1}{1 + e^{-x}}$$

The quality of the trained model is measured using the Root Mean Square Error (RMSE) [20]. RMSE is sensitive to outliers in the data, and its expression is:

$$\text{RMSE} = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(Y_i - \hat{Y}_i)^2}$$

Where N is the number of samples; Y_i is the true value; Ŷ_i is the predicted value.

The Monte Carlo program was used to simulate and calculate 520 sets of training data. Among these, 470 sets were used to train the BPNN, and the remaining 50 sets were used to test the BPNN prediction model. The initial training model parameter selection is shown in Table 3 [TABLE:3]. The training model sets first-order and second-order momentum factors. By monitoring changes in the loss function, the learning rate is automatically adjusted: if the loss function stagnates for 20 epochs, the learning rate is multiplied by 0.5 until it reaches 1e-6, achieving fine-grained learning rate adjustment in later training stages and improving final convergence quality. Simultaneously, L2 weight regularization is added to the hidden layer to penalize large weights and prevent overfitting. In terms of training strategy, EarlyStopping is implemented to automatically stop training and restore optimal weights when the validation set metric no longer improves, saving computation time while enhancing generalization performance.

5.3 Training Results

After constructing the prediction model, the neural network was optimized and trained to determine the appropriate number of hidden layers and neuron nodes per layer. The usual training approach involves testing different structures from simple to complex to find a neural network configuration with a smaller RMSE value. After multiple rounds of parameter tuning and training, a three-layer structure of 64:64:64 was finally determined. Fig. 15 [FIGURE:15] shows the adaptive changes of the loss function and learning rate during training iterations. With the EarlyStopping mechanism, the model reached its optimum at Epoch 967 and stopped iterating. Fig. 16 [FIGURE:16] shows the agreement between true values and predicted values for the 5 output layers. Output1-Output5 correspond to neutron capture rate, beta electron escape rate, gamma photon generation rate, probability of electron generation by gamma photons, and escape rate of electrons generated by gamma photons, respectively. The RMSE values for the training outputs were 0.0000158, 0.000976, 0.0000853, 0.0000983, and 0.000542, respectively. This indicates that the neural network is effective and can well reflect the mapping relationship between the parameters burnup time, emitter radius, number of emitter layers, and the neutron capture rate, beta electron escape rate, gamma photon generation rate, probability of electron generation by gamma photons, and escape rate of electrons generated by gamma photons. It can provide data support for subsequent research on Rh-SPND signal current variation with in-core burnup time.

5.4 Prediction Results of the Model for Rh-SPND Sensitivity Variation with Time

As shown in Fig. 17 [FIGURE:17], comparison results between Monte Carlo calculated values and model-predicted values for Rh-SPND sensitivity with a rhodium wire radius of 0.4 mm demonstrate that when burnup time is less than 9 years, calculated and predicted values are basically identical. When burnup time exceeds 9 years, predicted values become larger than calculated values, showing some deviation. Overall, the prediction model achieves accurate prediction of Rh-SPND sensitivity variation with time. Fig. 18 [FIGURE:18] shows model prediction results for Rh-SPND sensitivity with rhodium wire radii ranging from 0.1 mm to 1.0 mm over burnup time. As burnup time gradually increases, the linearity of Rh-SPND sensitivity change trends weakens, and the rate of change gradually decreases. Moreover, within 10 years of burnup time and at a neutron flux of 1×10¹⁴ n/(cm²·s), smaller rhodium wire radii exhibit larger sensitivity change ranges. Specifically, Rh-SPND sensitivity with a rhodium wire radius of 0.1 mm decreases by 51.3%, while that with a radius of 1 mm decreases by 25.2%. The main reason for this difference is the neutron self-shielding effect. Fig. 18 reveals the variation pattern of Rh-SPND sensitivity with burnup time. To achieve real-time and accurate monitoring of core neutron flux, time correction of Rh-SPND sensitivity is very necessary, and this correction must consider emitter radius and reactor neutron flux level.

6 Conclusion

This study presents a comprehensive investigation into the long-term variation of signal current in Rhodium Self-Powered Neutron Detectors (Rh-SPNDs) under extended in-core burnup conditions. A combination of Monte Carlo simulations, layered material modeling, and neural network-based prediction was employed to develop a high-accuracy, data-driven sensitivity model. The key conclusions can be summarized as follows: First, emitter material composition undergoes significant changes during long-term irradiation due to neutron-induced transmutation and radioactive decay, affecting both beta and gamma electron generation and escape behavior. Second, a layered burnup model reveals that burnup rate is radially non-uniform, with outermost layers experiencing up to 66% higher depletion compared to the core. This gradient leads to a gradual shift in beta electron production toward the emitter center over time. Third, the contribution of prompt current and reactor gamma-induced interference current to the total SPND signal was evaluated. While prompt gamma electrons show some sensitivity to burnup, their overall effect remains limited. Reactor gamma-induced electrons contribute less than 0.3% of signal variation and can be neglected for practical prediction purposes. Fourth, a Back Propagation Neural Network (BPNN) was developed to predict SPND sensitivity across different burnup durations and emitter geometries. The model demonstrated excellent agreement with Monte Carlo simulation results, with maximum relative error below 2.3%. Finally, model predictions show that smaller emitter radii lead to greater sensitivity degradation, with a 51.3% decrease for 0.1 mm wires and 25.2% for 1.0 mm wires over 10 years, highlighting the necessity of geometry-based compensation or replacement strategies for long-term SPND deployment. In conclusion, this study provides a reliable framework for predicting Rh-SPND performance degradation due to burnup. The developed BPNN model, grounded in physical simulation and enriched by data-driven learning, offers a practical tool for optimizing SPND deployment and calibration in real-world nuclear reactors. The methodology is generalizable and may be extended to other detector materials and configurations in future work.

Funding

This work was supported by the Fundamental Research Funds for the Central Universities of China (lzujbky-2023-stlt01), and Research on High-Temperature-Resistant Ultra-Compact Self-Powered Neutron Detection Technology for Fuel Irradiation Tests (CNNC-LCKY-2024-079).

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